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Review: Standard forms of expressions. We can write expressions in many ways, but some ways are more useful than others A sum of products (SOP) expression contains: Only OR (sum) operations at the “outermost” level Each term that is summed must be a product of literals

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Occasionally, we don’t care what the value of a function is for certain minterms.

When a certain input(s) will never happen. E.g. when dealing with Binary-coded decimal (BCD), the inputs for 1010-1111 (10-15) will never occur.

When a certain input(s) will occur, but we don’t care what the output will be in response to them. E.g. imagine a circuit which counts votes and has two outputs: a Yes/No output and a output which indicates ‘Tie’. If the vote is a tie, we don’t care whether the Yes/No output is 1 or 0.

We can either include or exclude these minterms in our function, whichever allows us to create the simplest representation.

On our K-map, we represent these minterms with an ‘x’ to indicate that it may or may not be grouped.

We can use K-maps to find the minimal Sum of Products (MSP) given some representation of a function.

The minimal Product of Sums of a function can be found by complementing the MSP of that function’s complement. Thus K-maps can be used to find a minimal PoS.

Don’t-care conditions allow us to simplify the expression (and thus the circuit) for functions where we’re only concerned about some of the inputs. This can result in multiple functions which are algebraically unequal, but both of which correctly meet the specifications of our function.